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A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is

1. mg(h + d) − 1/2 kd²
2. mg(h − d) − 1/2 kd²
3. mg(h − d) + 1/2 kd²
4. mg(h + d) + 1/2 kd²

Correct answer: mg(h + d) − 1/2 kd²

Solution

The net work done is the sum of the work done by gravity and the elastic potential energy stored in the spring. Gravity does work equal to mg(h + d), and the spring stores elastic potential energy equal to (1/2)kd². The net work is therefore mg(h + d) − (1/2)kd².

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